THE FACETING OF A GEMSTONE ONLY  
APPEARS COMPLEX AND CRITICAL 

To the average person, viewing a magnificently
faceted diamond or colored gemstone, the complexity
appears awesome. How do you manage to cut all
those bright, tiny facets? It must take enormous talent.
  They are queries often heard by faceters.
     Usually a faceter will nod smugly and make light
of his or her apparent genius, a mode too often dedicated
to keeping you awed.  If the question is posed to an
honest gemcutter, s/he might respond with a famous
Japanese idiom, "HAI." HAI is a marvelous all-purpose
expression that means, "yeh, yeh . . . I suppose so . . .
OK . . . I'm cool . . . I get it . . . I'm with you . . .go ahead
. . . etc."
Faceting methodology consists of mounting a gem crystal
on a metal dowel, (dopstick), which fits into a quill, then
rigidly addressing the Height-Angle-Index triangle with the
faceting machine, and touching  the locked-in-place crystal
to abrasive laps in two sequential operations, faceting first
the top (called the "crown") and then the bottom (called the
"pavilion").
In faceting, HAI is much more than a casual idiom. It is an
absolute ruling principle, expressed as an acronym with it's
significance focused on "go ahead."  When a faceter can say
HAI to his or her faceting progress, it means "OK to go ahead"
(and facet) because the vital triangle is in place (as shown in "B"
above) with the gemcutter  incontrol of the three principle elements
of faceting: 
H -- height
A--angle
I--index.
  Height controls the depth to which a facet is cut and this enables a
faceter to establish even, uniform rows of same sized, same depth
facets.   Angle establishes the plane upon which each facet is cut
because optics and performance is so dependant on each facet(s)
possessing just the right amount of plane or slant.. Index refers to the
placement of the facets around the shape or outline i.e., a round
brilliant cut stone, like most diamonds, shows eight main facets when viewed
straight down in "plan view."  
These three important elements are more fully explained below.

Four Simple Steps . . .

For the most part, you can take all the mysticism and incantation,
secrecy and ritual and downright nonsense, roll it up into a ball and
toss same in a faceting scrap heap.  Faceting consists of four simple
elements:
1) a person to set and hold the machine
2) the faceting machine
3) abrasive disks to do the cutting and polishing
4) a piece of natural or man-made crystal to cut 
It may look complex, but one must merely glue or attach a stone
to a metal dowel (called a dopstick, then set the machine's mast
(for H), adjust the protractor or quill position (for A), place the
trigger grip in the numbered notch in an index wheel (for I). Next, s/he
lowers the stone to the abrasive lapwheel and monitors cutting
and polishing progress. There really isn't much more to it than
that which is why faceting can actually be learned in a few hours.
That learning process will allow one to cut the most famous
and easiest cut of all, the famed American round brilliant whose
shape and appearance symbolizes and dominates the entire field
of gemcutting. Truth is, nine out of 10 gemstones are cut in the
round brilliant mode or one of its variations.
How is this possible?  The answer is simple.  Modern faceting
machines are actually milling machines (it's not by chance that
the leading faceting machine manufacturers are machinists by
trade).
All three HAI controls (mast, quill, index wheel)are
routinely locked in during setup before a faceter even starts
to cut.  As a result, the faceter needs only "patience,"  the
ability and mind set to hold the locked-in-place stone against
an abrasive wheel and watch the progress.  Among
faceters " . . . cut and look . . . cut and look . . . " is a time honored
reality. 

The Four P's of Gemstone Analysis . . .

If you never cut a gemstone but want to be able to evaluate
one professionally, keep in mind that  any cut--diamond or
colored stone--is evaluated on the basis of what I call
the 5 P's of cut appraisal:  
1)--Points (edges and intersections meet precisely which proves
that facets have been cut evenly and uniformly)  
2)--Proportions (for the height of most faceted gems the top part
represents 1/3 and the bottom part represents 2/3
3--Polish (a fine polish proves that the previous steps, too, were
done properly)  
4)--Positioning (an astute faceter has studied the gem crystal and
oriented to conform with optical laws and to minimize the visibility
and interference of imperfections
and, finally,
5--Performance (if the vital angles are observed, the stone's facets
reflect and refract the maximum amount of external and internal light
i.e., it will perform optically - even when tilted or tipped away from
normal. This reflective capability contrast with an uninteresting piece of
see-through glass when the gem is viewed straight down through the table).
     All of a faceter's efforts are focused through HAI to accomplish
these Five P's mentioned above.  Here's how it's done.

Faceting Fundamentals . . .

Faceting methodology consists of (A) cutting appropriate angles on the top
and bottom of a gem crystal, because (B) the faceting machine forms a right
triangle that controls the stone's angle on the abrasive disk, and (3) a faceter
to hold the stone against the turning lap wheel and monitor progress in cutting
the "crown" i.e, the top of the gem, and the "pavilion" i.e., the bottom of the gem.
Obviously, traditional faceting is a two-step process.
..

H = Height
As explained above, very faceting machine must form a right triangle so the target angle will appear at
the stone-abrasive disk intersection.  To accomplish this, the faceting head is raised on its mast  (in a protractor machine) or the quill's tailpiece in a jamb peg machine is placed in an elevated slot on the back- board jamb. In both cases the quill's are locked at an elevation consistent with the stone's diameter or width.  This action coordinates the machine's quill to the stone so height is no longer an issue.
A--Angle.
Once the quill's elevation is established, angle setting becomes a cinch.  The mechanical protractor stop is set to the targeted angle or the jamb peg's quill tailpiece is slipped into the appropriately numbered angle slot.   This effectively assures that the cut facet will finish up at the desired angle.   Thus, setting angles involves merely a simple dial-up task or a put-it-in-the-right-slot proposition.  Your greatest danger consists in setting the angle position wrong.
I--Index.  
Placing all those "tiny" facets around and about a faceted gem demands little more than slipping a trigger into a numbered gear notch.  If the instructions tell you to put the trigger in the "2" notch to cut a particular facet, that's what you do and the task is done . . . the faceting machine will dutifully cut a nice particular facet at the right angle and at the place you want.   Again, your greatest danger consists in placing the trigger in the wrong notch.  
       That's it!  Observe HAI on every facet and you'll achieve the 4 P's every time you cut a stone.  As for the supplementary heady stuff concerning proper angles, conversion of notch numbers from one index
gear to the next, reflectivity, etc., well, that's a cinch, too. 
If you're not a mathematician or if you don't want to memorize a lot of formulas, refer to the FacMath utilities in the Reference Section and your PC computer will make you a wizard in a minute or so - and you won't make any arithmetical mistakes either.

                                                       

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